A016007 -id:A016007 - cp's OEIS frontend

A015999 a(n) = (tau(n^5) + 4)/5.

1, 2, 2, 3, 2, 8, 2, 4, 3, 8, 2, 14, 2, 8, 8, 5, 2, 14, 2, 14, 8, 8, 2, 20, 3, 8, 4, 14, 2, 44, 2, 6, 8, 8, 8, 25, 2, 8, 8, 20, 2, 44, 2, 14, 14, 8, 2, 26, 3, 14, 8, 14, 2, 20, 8, 20, 8, 8, 2, 80, 2, 8, 14, 7, 8, 44, 2, 14, 8, 44, 2, 36, 2, 8, 14, 14, 8, 44, 2, 26, 5, 8, 2, 80, 8, 8

Offset: 1

Robert G. Wilson v

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A018892, A015995, A015996, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016012.

with(numtheory): A015999:=n->(tau(n^5)+4)/5: seq(A015999(n), n=1..80); # Wesley Ivan Hurt, Apr 10 2015

(DivisorSigma[0, Range[80]^5]+4)/5 (* Wesley Ivan Hurt, Apr 10 2015 *)

A015999(n) = (numdiv(n^5)+4)/5;
for(n=1, 10000, write("b015999.txt", n, " ", A015999(n)));
\\ Antti Karttunen, Jan 17 2017

from sympy import divisor_count
def a(n): return (divisor_count(n**5) + 4)//5
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Apr 14 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A016005 a(n) = (tau(n^9)+8)/9.

Original entry on oeis.org

1, 2, 2, 3, 2, 12, 2, 4, 3, 12, 2, 22, 2, 12, 12, 5, 2, 22, 2, 22, 12, 12, 2, 32, 3, 12, 4, 22, 2, 112, 2, 6, 12, 12, 12, 41, 2, 12, 12, 32, 2, 112, 2, 22, 22, 12, 2, 42, 3, 22, 12, 22, 2, 32, 12, 32, 12, 12, 2, 212, 2, 12, 22, 7, 12, 112, 2, 22, 12, 112, 2, 60, 2, 12

Offset: 1

Robert G. Wilson v

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A015996, A015999, A016001, A016002, A016003, A016006, A016007, A016008, A016009, A016012.

a[n_] := (DivisorSigma[0, n^9] + 8)/9; Array[a, 100] (* Amiram Eldar, Jan 27 2025 *)

A016005(n) = (numdiv(n^9)+8)/9; \\ Antti Karttunen, Jan 17 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A015996 (tau(n^4) + 3)/4, where tau = A000005.

Original entry on oeis.org

1, 2, 2, 3, 2, 7, 2, 4, 3, 7, 2, 12, 2, 7, 7, 5, 2, 12, 2, 12, 7, 7, 2, 17, 3, 7, 4, 12, 2, 32, 2, 6, 7, 7, 7, 21, 2, 7, 7, 17, 2, 32, 2, 12, 12, 7, 2, 22, 3, 12, 7, 12, 2, 17, 7, 17, 7, 7, 2, 57, 2, 7, 12, 7, 7, 32, 2, 12, 7, 32, 2, 30, 2, 7, 12, 12, 7, 32, 2, 22, 5, 7, 2, 57, 7, 7

Offset: 1

Robert G. Wilson v

nonn

If n is prime, a(n) = 2 since a(p) = (tau(p^4)+3)/4 = (5+3)/4 = 2. - Wesley Ivan Hurt, Nov 16 2013

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A018892, A015995, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A016012, A016020.

A015996 := proc(n)
        (numtheory[tau](n^4)+3)/4 ;
end proc; # R. J. Mathar, May 09 2013

Table[(DivisorSigma[0, n^4] + 3)/4, {n, 100}] (* Wesley Ivan Hurt, Nov 16 2013 *)

A015996(n) = (numdiv(n^4)+3)/4;
for(n=1, 10000, write("b015996.txt", n, " ", A015996(n)));
\\ Antti Karttunen, Jan 17 2017

a(n) = (A000005(n^4) + 3)/4.

Definition corrected by Vladeta Jovovic, Sep 03 2005

A016001 a(n) = (tau(n^6)+5)/6.

Original entry on oeis.org

1, 2, 2, 3, 2, 9, 2, 4, 3, 9, 2, 16, 2, 9, 9, 5, 2, 16, 2, 16, 9, 9, 2, 23, 3, 9, 4, 16, 2, 58, 2, 6, 9, 9, 9, 29, 2, 9, 9, 23, 2, 58, 2, 16, 16, 9, 2, 30, 3, 16, 9, 16, 2, 23, 9, 23, 9, 9, 2, 107, 2, 9, 16, 7, 9, 58, 2, 16, 9, 58, 2, 42, 2, 9, 16, 16, 9, 58, 2, 30, 5, 9, 2, 107, 9

Offset: 1

Robert G. Wilson v

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A015996, A015999, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A016012.

a[n_] := (DivisorSigma[0, n^6] + 5)/6; Array[a, 100] (* Amiram Eldar, Jan 27 2025 *)

A016001(n) = (numdiv(n^6)+5)/6;
for(n=1, 10000, write("b016001.txt", n, " ", A016001(n)));
\\ Antti Karttunen, Jan 17 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A016009 a(n) = (tau(n^13)+12)/13.

Original entry on oeis.org

1, 2, 2, 3, 2, 16, 2, 4, 3, 16, 2, 30, 2, 16, 16, 5, 2, 30, 2, 30, 16, 16, 2, 44, 3, 16, 4, 30, 2, 212, 2, 6, 16, 16, 16, 57, 2, 16, 16, 44, 2, 212, 2, 30, 30, 16, 2, 58, 3, 30, 16, 30, 2, 44, 16, 44, 16, 16, 2, 408, 2, 16, 30, 7, 16, 212, 2, 30, 16, 212, 2, 84, 2, 16

Offset: 1

Robert G. Wilson v

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A015996, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016012.

a[n_] := (DivisorSigma[0, n^13] + 12)/13; Array[a, 100] (* Amiram Eldar, Jan 27 2025 *)

A016009(n) = (numdiv(n^13)+12)/13;
for(n=1, 10000, write("b016009.txt", n, " ", A016009(n)));
\\ Antti Karttunen, Jan 17 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A016012 a(n) = (tau(n^n)+n-1)/n.

Original entry on oeis.org

1, 2, 2, 3, 2, 9, 2, 4, 3, 13, 2, 28, 2, 17, 18, 5, 2, 40, 2, 44, 24, 25, 2, 77, 3, 29, 4, 60, 2, 994, 2, 6, 36, 37, 38, 149, 2, 41, 42, 125, 2, 1894, 2, 92, 94, 49, 2, 198, 3, 104, 54, 108, 2, 167, 58, 173, 60, 61, 2, 7505, 2, 65, 130, 7, 68, 4558, 2, 140, 72, 5114

Offset: 1

Robert G. Wilson v

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A015996, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A016025.

f[j_, n_] := (DivisorSigma[0, n^j] + j - 1)/j; Table[ f[n, n], {n, 96}]

A016012(n) = (numdiv(n^n)+n-1)/n;
for(n=1, 10000, write("b016012.txt", n, " ", A016012(n)));
\\ Antti Karttunen, Jan 17 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A126098 Where records occur in A018892.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 30, 60, 120, 180, 210, 360, 420, 840, 1260, 1680, 2520, 4620, 7560, 9240, 13860, 18480, 27720, 55440, 83160, 110880, 120120, 180180, 240240, 360360, 720720, 1081080, 1441440, 1801800, 2042040, 2882880, 3063060, 4084080, 5405400, 6126120, 12252240, 18378360, 24504480

Offset: 1

N. J. A. Sloane, Mar 05 2007

nonn

Remarkably similar to but ultimately different from A018894. - Jorg Brown and N. J. A. Sloane, Mar 06 2007
This sequence represents "where records occur" for a number of sequences in addition to A018892 including the following: A015995, A015996, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A048691, A048785, A063647, A117677, A144943. - Ray Chandler, Dec 04 2008
Subsequence of A025487. - Ray Chandler, Sep 05 2008
Also record-setting elements of tau(n^2) (just as A002182 gives the record-setting elements of tau(n)). The point is that A018892 is (tau(n^2) + 1)/2. As tau(n^2) is odd, the record-setting elements of A018892 are also the record setting elements of tau(n^2). - Allen Tracht, Jan 20 2009

Ray Chandler, Table of n, a(n) for n = 1..582
Jorg Brown, Comparison of records in sigma(n)/phi(n) and A018892

Cf. A018892, A126097. Equals A117010(n) + 1.

More terms from Jorg Brown (jorg(AT)google.com) and T. D. Noe, Mar 05 2007

a(27) corrected by hupo001(AT)gmail.com, Jan 10 2008

A016006 a(n) = (tau(n^10)+9)/10.

Original entry on oeis.org

1, 2, 2, 3, 2, 13, 2, 4, 3, 13, 2, 24, 2, 13, 13, 5, 2, 24, 2, 24, 13, 13, 2, 35, 3, 13, 4, 24, 2, 134, 2, 6, 13, 13, 13, 45, 2, 13, 13, 35, 2, 134, 2, 24, 24, 13, 2, 46, 3, 24, 13, 24, 2, 35, 13, 35, 13, 13, 2, 255, 2, 13, 24, 7, 13, 134, 2, 24, 13, 134, 2, 66, 2, 13

Offset: 1

Robert G. Wilson v

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A015996, A015999, A016001, A016002, A016003, A016005, A016007, A016008, A016009, A016012.

a[n_] := (DivisorSigma[0, n^10] + 9)/10; Array[a, 100] (* Amiram Eldar, Jan 27 2025 *)

A016006(n) = (numdiv(n^10)+9)/10;
for(n=1, 10000, write("b016006.txt", n, " ", A016006(n)));
\\ Antti Karttunen, Jan 17 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A016008 a(n) = (tau(n^12)+11)/12.

Original entry on oeis.org

1, 2, 2, 3, 2, 15, 2, 4, 3, 15, 2, 28, 2, 15, 15, 5, 2, 28, 2, 28, 15, 15, 2, 41, 3, 15, 4, 28, 2, 184, 2, 6, 15, 15, 15, 53, 2, 15, 15, 41, 2, 184, 2, 28, 28, 15, 2, 54, 3, 28, 15, 28, 2, 41, 15, 41, 15, 15, 2, 353, 2, 15, 28, 7, 15, 184, 2, 28, 15, 184, 2, 78, 2, 15

Offset: 1

Robert G. Wilson v

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A015996, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016009, A016012.

a[n_] := (DivisorSigma[0, n^12] + 11)/12; Array[a, 100] (* Amiram Eldar, Jan 27 2025 *)

A016008(n) = (numdiv(n^12)+11)/12;
for(n=1, 10000, write("b016008.txt", n, " ", A016008(n)));
\\ Antti Karttunen, Jan 17 2017

Definition corrected by Vladeta Jovovic, Sep 03 2005

A016018 Least k such that (tau(k^3)+2)/3=n.

Original entry on oeis.org

1, 2, 4, 8, 16, 6, 64, 128, 256, 12, 1024, 2048, 4096, 24, 16384, 32768, 36, 48, 262144, 524288, 1048576, 30, 4194304, 72, 16777216, 192, 67108864, 134217728, 268435456, 384, 144, 2147483648, 4294967296, 216, 17179869184, 34359738368, 68719476736

Offset: 0

Robert G. Wilson v

nonn

Cf. A015995, A015996, A015999, A016001, A016002, A016003, A016005, A016006, A016007, A016008, A016009, A016012, A016017, A016020 & A016025

More terms from Robert G. Wilson v, Aug 06 2005
Definition corrected by Vladeta Jovovic, Sep 03 2005
Extended by Ray Chandler, Sep 05 2008

cp's OEIS Frontend

A015999 a(n) = (tau(n^5) + 4)/5.

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A016005 a(n) = (tau(n^9)+8)/9.

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A015996 (tau(n^4) + 3)/4, where tau = A000005.

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A016001 a(n) = (tau(n^6)+5)/6.

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A016009 a(n) = (tau(n^13)+12)/13.

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A016012 a(n) = (tau(n^n)+n-1)/n.

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A126098 Where records occur in A018892.

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A016006 a(n) = (tau(n^10)+9)/10.

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